Abyss Dive (2D)

Pressure, density and buoyancy

Sea water is slightly compressible: ρ(p) = ρ₀ / (1 − p/K) with bulk modulus K ≈ 2.34 GPa. Integrating the hydrostatic equation dp/dz = ρ g gives a closed form,

so at 10 km the pressure is about 1,000 bar and the density about 4 % above the surface value. A submersible of mass m and displaced volume V feels a net weight (m − ρV)g and quadratic drag ½ρC_dAv²; the page integrates it with RK4 including the added mass of the displaced water. Terminal speed is v_t = √(2 (m − ρV) g / (ρ C_d A)). Because ρ rises with depth, a sub that is slightly heavy at the surface can reach neutral buoyancy and hover.

Light, temperature and sound

Each colour band decays as I = I₀ e^−Kz (Beer-Lambert) with K about 0.45 /m for red and 0.025 /m for blue clear water, so red is gone within tens of metres. Temperature follows a smooth thermocline from the surface value to about 2 C. Sound speed is the Mackenzie (1981) formula c(T, S, D), whose minimum is the SOFAR channel.

Honest simplifications

• One idealised, horizontally uniform column: no currents, salinity changes, internal waves or seasonal thermoclines. Salinity is fixed at 35.
• The hull is treated as incompressible; real pressure hulls shrink slightly and syntactic foam is sized to compensate.
• Light attenuation uses four representative bands, not the full spectrum, and no scattering by particles beyond the turbidity factor.
• Creature silhouettes are decorative markers of the typical depth zones, not a biological model. Time warp speeds the dive so that kilometres can be covered in minutes.

• Run Heavy dive to the seabed and watch the colours vanish: red first, blue last, then complete darkness below about 1,000 m.
• Run Neutral buoyancy hover: the sub sinks, slows and stops where the water density equals its mean density.
• Drop the ballast slider mid-dive to release weight and rise again.
• Raise turbidity to 6 and see the sunlit zone shrink to a few tens of metres.